Operations management chapter 13

Compute when carrying costs are expressed as a percentage of price, determine best purchase quantity

1. begin with the lowest unit price, compute min points for each price range until you find a feasible min point. 2. if min point for lowest unit price is feasible, it is the optimal order quantity. if min point is not feasible in lowest price range, compare the total cost at the price break for all lower prices with the total cost of the feasible min point. The quantity that yields the lowest total cost is the optimum. to compute optimal order quantity and the total annual cost (Follow Example 6 on page 576-577)

Compute overall EOQ

1. compute the common min point 2. only one of the unit prices will have the min point in its feasible range since the ranges do not overlap. Identify the range. A. if the feasible min point is on the lowest price range, that is the optimal order quantity. B. if the feasible min point is in any other range, compute the total cost for the min point and for the price breaks of all lower unit costs. Compare the total costs, the quantity (min point or price break) that yields the lowest total cost is the optimal order quantity. Compute the optimal order quantity and the total cost (compute common minimum Q= sqrt(2DS/H)) (Example 5 page 575)

Functions of inventory: 8 types

1. meet anticipated customer demand- a customer can be a person who walks in off the street to buy a new stereo system a mechanic who requests a tool at a tool crib, or manufacturing operation. These inventories are referred to as anticipation stocks because they are held to satisfy expected demand. 2. To smooth production requirements- firms that experience seasonal patterns in demand often build up inventories during preseason periods. These inventories are aptly named seasonal inventories. companies that process fresh fruits and vegetables deal with seasonal inventories. so do stores that sell greeting cards, skis, snowmobiles or Christmas trees 3. To decouple operations- historically manufacturing firms have used inventories as buffers between successive operations to maintain continuity of production that would otherwise be disrupted by events such as breakdowns of equipment and accidents that cause a portion of the operation to shut down temporarily. The buffers permit other operations to continue temporarily while the problem is resolved. Similarly, firms have used buffers of raw materials to insulate production from disruption in deliveries from suppliers, and finished goods inventory to buffer sales operations from manufacturing disruptions. More recently, companies have taken a closer look at buffer inventories, recognizing the cost and space they require, and realizing that finding and eliminating sources of disruptions can greatly decrease the need from decoupling operations. Inventory buffers are also important in supply chains. Careful analysis can reveal both points where buffers would be most useful and points where they would merely increase costs without adding value. 4. to protect against stockouts- delayed deliveries and unexpected increases in demand increase the risk of shortages. Delays can occur because of weather conditions, supplier stockouts, deliveries of wrong materials, quality problems and so on. The risk of shortages can be reduced by holding safety stocks, which are stocks, which are stocks in excess of expected demand to compensate for variabilities in demand and lead time. 5. To take advantage of order cycles- to minimize purchasing and inventory costs, a firm often buys in quantities that exceed immediate requirements. This necessitates storing some or all of the purchased amount for later use. similarly, it is usually economical to produce in large rather than small quantities. Again, the excess output must be stored for later use. Thus, inventory storage enables a firm to buy and produce in economic lot sizes without having to try to match purchases or production with demand requirements in the short run. this results in periodic orders or order cycles. 6. To hedge against price increases- occasionally a firm will suspect that a substantial price increase is about to occur and purchase larger-than-normal amounts to beat the increase. The ability to store extra goods also allows a firm to take advantage of price discounts for larger orders. 7. To permit operations- the fact that production operations take a certain amount of time (they are not instantaneous) means that there will generally be some work-in-process inventory. In addition, intermediate stocking of goods- include raw materials, semi finished items, and finished goods at production sites, as well as goods stored in warehouses- leads to pipeline inventories throughout a production- distribution system. Littles law can be useful in quantifying pipeline inventory. it states that the average amount of inventory in a system is equal to the product of the average rate at which inventory units leave the system and the average time a unit is in the system. Thus, if a unit is in the system for an average of 10 days, and the demand rate is 5 units per day, the average inventory is 50 units: 5 units/day X 10 days=50 units 8. To take advantage of quantity discount- suppliers may give discounts on large orders (page 558)

4 determinants of reorder point quantity

1. the rate of demand (usually based on a forecast) 2. the lead time 3. the extent of demand and or lead time variability 4.the degree of stockout risk acceptable to management compute at what point should you reorder. (page 578 example 7)

management has two basic functions concerning inventory

1. to establish a system to keep track of items in inventory 2. to make decisions about how much and when to order. (page 559)

Compute ROP for variable demand rate and variable lead time and get a specific service level

page 598 problem 6

compute fixed order interval

use when an order interval is given along with the demand rate, lead time, quantity on hand at order time. How much should be ordered? what is the average amount of safety stock? page 599 problem 8

compute Expected amount of shortage for a given lead time service level

use same info used to compute ROP, with one additional piece of info. use table 13.3. assumes the distribution of lead time demand can be represented by a normal distribution. expected number of units short in each order cycle is given by this formula./ (Expected number of units short per order cycle)= (standardized number of units short obtained from table 13.3)* (standardized deviation of lead time demand) page 582 and example 10 on page 584

compute Reorder point

use when demand rate, lead time and desired service level or stockout risk are given (page 597 problem 4)

compute single- period

use when probability distribution or empirical distribution for demand for a perishable item is given along with unit shortage and excess costs, or info that can be used to calculate them. Compute optimal service level, exact stocking level, if distribution is Poisson or empirical (page 600, problem 9)

Compute shortages and service levels

use when problem asks for number of units short per order cycle, or per year. Find average number of units short per year that will be consistent with the specified annual service level. what Average number of units short per cycle will provide the desired annual service level. What lead time service level is necessary for percent annual service level. page 599 problem 7

perpetual inventory system

(Also known as a continual system) system that keeps track of removals from inventory continuously, thus monitoring current levels of each item so the system can provide information on the current level of inventory for each item. When the amount on hand reaches a predetermined min, a fixed quantity, Q, is ordered. Advantage- control provided by the continuous monitoring of inventory withdrawals. another advantage is the fixed order quantity management can determine an optimal order quantity. Disadvantage- added cost of record keeping and physical count of inventories must still be performed periodically to verify records because of possible errors, pilferage, spoilages and other factors that can reduce the effective amount of inventory. Ex- bank transactions such as customer deposits and withdrawals are examples of continuous recording of inventory changes. (page 560)

Return on investment

(ROI) one widely used measure of managerial performance. this is profit after taxes divided by total assets. Because inventories may represent a significant portion of total assets, a reduction of inventories can result in a significant increase in ROI. page 557

Single period model

(newsboy problem) model for ordering of perishables and other items with limited useful life. Shortage and excess (page 588)

Compute optimal run size, minimum total annual cost for carrying and setup. Cycle time for the optimal run size. and Run time

(page 572) Example 4/ compute the economic run quantity, approx how many runs per year, max inventory level, the length of pure consumption portion of the cycle (page 595 Problem 2)

APICS recommends guidelines for inventory record accuracy

+or - .2 percent for A items, +or - 1percent for B items, and + or - 5 percent for C items. A items counted frequently, B are less, and C are the least frequent. Events that trigger physical count of inventory include an out of stock report written on an item indicated by inventory records to be in stock, an inventory report that indicates a low or zero balance of an item and specified level of activity. (page 565)

compute fixed - interval model

Amount to order= Expected demand during protection interval + safety stock - Amount on hand at reorder time. Page 587 and Example 13

Excess cost

Difference between purchase cost and salvage value of items left over at the end of a period. =original cost per unit- salvage value per unit. there is cost with disposing of excess items, salvage value will be negative and increase the excess cost per unit (page 588)

EOQ in terms of min cost

EOQ is fairly robust; the total cost curve is relatively flat near the EOQ, especially to the right of the EOQ. even if the order quanittiy differs from the actual EOQ, total costs will not increase much at all. Particularly true for quantities larger than the real EOQ, becasue the total cost curve rises very slowly to the right of the EOQ. Because the total cost curve is relatively flat around the EOQ, there can be some flexibility to modify the order quantity a bit from the EOQ without incurring much of an increase in total cost. (page 570)

Shortage cost

Generally the unrealized profit per unit. = Revenue per unit-cost per unit (page 588)

performance measures to judge effectiveness of inventory management

Most obvious is customer satisfaction which they might measure by the number and quantity of backorders and or customer complaints., a widely used measure is; Inventory turnover- ratio of average cost of goods sold to average inventory investment. The ratio indicates how many times a year the inventory is sold. Generally The Higher the ratio, the better, because that implies more efficient use of inventories. Desirable number of turns depends on the industry and what the profit margins are. The higher the profit margins, the lower the acceptable number of inventory turns, and vice versa. another useful measures is days of inventory on hand, a number that indicates the expected number of days of sales that can be supplied from existing inventory. a balance is desirable; a high number of days might imply excess inventory, while a low number might imply a risk of running out of stock. (page 559)

Compute optimal quantity and total annual cost of ordering and carrying the inventory

Page 570 Example 3/ compute oder quantity and number of workdays in an order cycle page 595 problem 1

kinds of inventories

Raw materials and purchased parts, partially completed goods, called work-in-process (WIP), Finished-goods inventories (manufacturing firms) or merchandise (retail stores), Tools and supplies, maintenance and repairs (MRO) inventory, Goods in transit to warehouses, distributors, or customers (pipeline inventory) page 557

Little's Law

The average amount of inventory in a system is equal to the product of the average demand rate and the average time a unit is in the system (page 558)

Two-bin system

Two containers of inventory; reorder when the first is empty. a perpetual system that is very elementary. Uses two containers for inventory. Items are taken from the first bin until its empty and then its time to reorder. an order card is placed at bottom of first bin.. the second bin contains enough stock to satisfy expected demand until the order is filled plus an extra cushion of stock that reduces chance of a stock out if the order is late or usage is greater than expected. Advantage- no need to record each withdrawal from inventory. Disadvantage- the reorder card may not be turned in for a variety of reasons, misplaced, the person forgets to turn it in. (page 560)

Reorder point (ROP)

When the quantity on hand of an item drops to this amount, the item is reordered... When to order? generally includes expected demand during lead time and an extra cushion of stock. In order to know when the reorder point has been reached, perpetual inventory monitoring is required. (page 578)

cycle counting

a physical count of items in inventory, another application of ABC concept is as a guide for cycle counting. THe purpose is to reduce discrepancies between the amounts indicated by inventory records and the actual quantities of inventory on hand. Key questions concerning cycle counting for management- 1. how much accuracy is needed? 2. when should cycle counting by performed? 3. who should do it? (page 565)

Turn over rate

a product that takes a long time to manufacture, or a long time to sell will have a low turnover rate. This is often the case with high-end retailers (high profit margins). supermarkets (low profit margins) have a fairly high turnover rate. There should be a balance between inventory investments and maintaining good customer service. Managers often use inventory turnover to evaluate inventory management performance; monitoring this metric over time can yield insights into changes in performance. (page 559)

Inventory

a stock or store of goods (page 556) in terms of dollars, the inventory of goods held for sale is one of the largest assets of a merchandising business page 557

Inventory ordering policies

address two basic issues of inventory management, which are how much to order and when to order. (page 566)

Purchase cost

amount paid to a vendor or supplier to buy the inventory. It is typically the largest of all inventory costs. (page 562)

variations

are present and must be taken into account. Uncertainties can be offset to some degree by holding safety stock although that adds to the cost of holding inventory.

carrying costs, ordering costs, total cost curve

carrying costs are linearly related to order size, ordering costs are inversely and nonlinearly related to order size, the total cost curve is U- shaped (page 568)

A-B-C approach

classifying inventory according to some measure of importance and allocating control efforts accordingly usually dollar value per unit multiplied by annual usage rate. A- Very important (usually 10-20% number of items in inventory and 50-60 percent of annual dollar value) a should receive close attention through frequent reviews of amounts on hand and control over withdrawals. B- moderately important. C- least important(50 -60% of numbers in inventory and 10-15 of annual dollar value) c gets only loose control like two-bin system, bulk orders. also used in customer service(page 563)

dependent demand items

components of finished products, rather than the finished products themselves page 556

Compute total Annual carrying cost

computed by multiplying the average amount of inventory on hand b the cost to carry one unit for one year, even though any given unit would not necessarily be held for a year. the average inventory is simply half of the order quantity the amount on hand decreases steadily from Q units to 0, for an average of (Q+2)/2 or Q/2 . H represents the average annual carrying cost per unit, the total annual carrying cost is = Q/2*H (page 568) follow Example 2 on (page 569) carrying cost is sometimes stated as a percentage of the price of an item rather than as a dollar amount per unit. as long as the percentage is converted into a dollar amount the EOQ formula is still appropriate. (page 570)

Inventory Management

core operations management activity, important for successful operations of most businesses and their supply chains, impacts operations, marketing and finance. poor inventory management hampers operations, diminishes customer satisfaction and increase operating costs (page 555)

Holding or carrying costs

cost to carry an item in inventory for a length of time, usually a year. costs include interest, insurance, taxes, depreciation, obsolescence, deterioration, spoilage, pilfrage, breakage, tracking, picking and warehousing costs (heat light rent security)also includes opportunity costs with having funds elsewhere. It is the variable portion of these costs that is pertinent. Stated in two ways- 1. as a percentage of unit price 2. as a dollar amount per unit range from 20-40% so to hold a $100 dollar item for one year could cost from $20 to $40. (page 562)

Ordering cost

costs of ordering and receiving inventory. the costs that vary with the actual placement of an order. Besides shipping costs, they include determining how much is needed, preparing invoices, inspecting goods upon arrival for quality and quantity and moving the goods to temporary storage. ordering costs are generally expressed as a fixed dollar amount per order, regardless of order size (page 562)

shortage costs

costs resulting when demand exceeds the supply of inventory; often unrealized profit per unit. not making a sale, loss of customer goodwill, late charges, backorder costs, cost of lost production or downtime is considered a shortage cost. easily run into hundreds of dollars a minute or more. Shortage costs are sometimes difficult to measure and they may be subjectively estimated. (page 562-563)

amount of safety stock needed for situation

depends on factors: 1. the average demand rate and average lead time 2. Demand and lead time variability 3. the desired service level For a given order cycle service level, the greater the variability in either demand rate or lead time, the greater the amount of safety stock that will be needed to achieve that service level. (page 579)

compute % risk of stockout during lead time

determine the value of z, Determine ROP (Follow example 9 on page 581)

compute optimal stocking level and stockout risk for that quantity (continuous stocking levels)

easiest to visualize when demand is uniform. the optimal stocking level is equivalent to a seesaw, the stocking level equalizes the cost weights. Service level is the probability that demand will not exceed the stocking level an computation of the service level is key to determining the optimal stocking level. service level= shortage cost per unit/ shortage cost per unit +excess cost per unit (page 589 and example 15

Point of sale (POS) systems

electronically record actual sales. record items at time of sale. Can greatly enhance forecasting and inventory management by relaying information about actual demand in real time, these systems enable management to make any necessary changes to restocking decisions. These systems are being increasingly emphasized as an important input to effective supply chain management by making this info available to suppliers. increase speed and accuracy they give managers continuous info on inventories, reduce the need for periodic review and order size determinations and improve the level of customer service by indicating the price and quantity of each item on the customers receipt. (560)

compute what value of z is appropriate, how much safety stock should be held? what reorder point should be used?

example 8 on page 580-581

compute Safety stock

extra inventory carried to reduce the probability of a stockout due to demand and or lead time variability (page 566) stock that is held in excess of expected demand due to variable demand and or lead time to reduce the risk of running out of inventory during lead time. the reorder point then increases by the amount of the safety stock: ROP= Expected demand during lead time + safety stock. If expected demand during lead time is 100 units and desired amount of safety stock is 10 units the ROP would be 110 units. Stockout protection is needed only during lead time (page 578)

compute standard deviation of demand

for the entire lead time is found by summing the variances of daily or weekly demands, and then finding the square root of that number because unlike variances, standard deviations are no additive page 582

typical firms

have about 30% of its current assets and perhaps as much as 90 percent of its working capital invested in inventory page 557

customer service level

increases as the risk of stockout decreases. a customer service level of 95% implies a stockout risk of 5 percent. (page 579)

Applicable or feasible total cost

initially on the curve with the highest unit price and then drops down, curve by curve at the price breaks, which are the min quantities needed to obtain the discounts. (page 574)

summary

inventory management is a core operations management activity. good inventory management is often the mark of a well-run organization. Inventory levels must be planned carefully in order to balance cost of holding inventory and the cost of providing reasonable levels of customer service. successful inventory management requires a system to keep track of inventory transactions, accurate information about demand and lead times, realistic estimates of certain inventory related costs, and priority system for classifying the items in inventory and allocating control efforts. Four classes of models are described; EOQ, ROP, fixed order interval, and single period models. the first three are appropriate if unused items can be carried over into subsequent periods. the single period model is appropriate when items cannot be carried over. EOQ models address the question of how much to order. The ROP models address the question of when to oder and helpful in situations that include variations in either demand rate or lead time. ROP models involve service level and safety stock considerations. When the time between orders is fixed. THE FOI model is useful for determining the order quantity. the single period model is used for items that have a shelf life of one period. The models present in this chapter are summarized in Table 13.5 on page 594 (page 593)

independent demand items

items that are ready to be sold or used. page 556

Universal product code (UPC)

most supermarkets, discount stores, department stores use periodic counting systems. Most have switched to computerized checkout systems using a laser scanning device that reads the UPC or bar code; printed on an item tag or on packaging. A zero on the left of the bar code identifies this as a grocery item, the first five numbers indicate the manufacturer and the last five numbers indicate the specific item. Items in small packages such as candy use a 6 digit number (page 560)

Disadvantages of fixed interval system

needs a larger amount of safety stock to protect against shortages during an entire order, increases carrying cost. high cost of periodic reviews. (page 588)

effective inventory decisions depend

on having good inventory record, good cost info, and good estimates of demand.(page 593)

2 main concerns about inventory management

one is the level of customer service, this is to have the right goods, in sufficient quantities, in the right place at the right time. The second is the costs of ordering and carrying inventories. (page 559)

Fixed order interval (FOI)

orders are placed at fixed time intervals. If demand is variable the order size will tend to vary from cycle to cycle instead of in an EOQ/ROP approach where the order size remains the same and the cycle length varies. Reasons for FOI - can produce savings in shipping costs and some situations can not use continuous monitoring of inventory level. (Page 585) fixed interval model - most frequently encountered situation. (page 586)

Compute ABC problems

page 564. Follow Example 1

compute expected number of units short per year

page 584 Example 11

Compute annual service level and amount of cycle safety stock that would provide a certain annual service level

page 585 example 12

compute risk of stockout at a certain time

page 587 follow example 14

compute optimal stocking level when demand is normally distributed

page 590 Example 16 and for discrete stocking levels example 17 page 591 and example 18 page 592

lean operation

page 593

record keeping

page 593

supply chain management

page 593

variation reduction

page 593

Compute ROP for constant demand and variable lead time and how many days of supply are on hand at the ROP

page 598 problem 5

Periodic system

physical count of items in inventory made at periodic intervals (weekly, monthly) in order to decide how much to order of each item. An advantage of this type of system is that orders for many items occur at the same time, which can result in economies in processing and shipping orders. Disadvantages- lack of control between reviews and need to protect against shortages between review periods by carrying extra stock. (page 560)

Compute Quantity Discounts

price reductions for larger orders offered to customers to induce them to buy in large quantities. price per item decreases as order quantity increases. if quantity discounts are offered, buyer must weigh the potential benefits or reduced purchase price and fewer orders that will result from buying in large quantities against the increase in carrying costs caused by higher average inventories. point for buyer is to minimize total cost, where total cost is the sum of carrying cost, ordering cost, and purchasing cost. separate U- shaped total cost curve for each unit price and including unit prices merely raises each curve by a constant amount (equation on page 573)/ (compute order size that will minimize total cost and if supplier offered discount what order size would minimize total cost. basic EOQ page 596 problem 3)

service level

probability that demand will not exceed supply during lead time. Service level= 100% - stockout risk (page 579)

Four basic inventory costs

purchase, holding, transaction (ordering) and shortage costs (page 562)

how much inventory to have

reflects a trade-off, how much money to tie up in inventory versus having it available for other uses. Factors related include purchase costs, holding costs, ordering costs, shortage and backlog costs, available space to store the inventory and return that can be had from other uses of the money. (page 595)

Inadequate control of inventory

results in under and over stocking of items. understocking results in missed deliveries, lost sales, dissatisfied customers, and production bottlenecks; overstocking unnecessarily ties up funds that might be more productive elsewhere. Although overstocking may appear to be the lesser of the two evils, the price tag for excessive overstocking can be staggering when inventory holding costs are high- as illustrated by the reading about the bin of gears at the beginning of the chapter- and matters can easily get out of hand. it is not unheard of for managers to discover that their firm has 10 year supply of some item (no doubt the firm got a good buy on it) (page 559)

other factors in classifying inventory items

risk of obsolescence, risk of stockout, the distance of a supplier and so on. (page 565)

Basic Economic Order quantity (EOQ) model

simplest of three models. used to identify a fixed order size that will min the sum of the annual costs of holding inventory and ordering inventory. The unit purchase price of items is generally not included in total cost because unit cost is unaffected by the order size unless quantity discounts are a factor. If holding costs are specified as a percentage of unit cost, then unit cost is indirectly included in total cost as part of holding costs. This model involves a number of assumptions. 1. only one product is involved 2. annual demand requirements are known. 3. Demand is spread evenly throughout the year so that the demand rate is reasonably constant 4. lead time is known and constant 5. Each order is received in a single delivery 6. there are no quantity discounts. A cycle begins with a receipt of an order of Q units, which are withdrawn at a constant rate over time. when quantity on hand is just enough for demand during lead time, an order for Q units is submitted to supplier. Orders are timed to avoid both excess stock and stockouts. balance between carrying costs and ordering costs. (page 566)

Radio frequency identification (RFID)

tags that are used to keep track of inventory in certain application (561)

Cycle stock

the amount of inventory needed to meet expected demand (page 566)

Economic Production Quantity (EPQ)

the batch mode is widely used in production. even in assembly operations, portions of the work are done in batches. in certain instances, the capacity to produce a part exceeds the part's usage or demand rate. as long as production continues inventory will continue to grow. Assumptions of EPQ model- orders units are received incrementally during production 1. only one item is involved. 2. Annual demand is known 3. the usage rate is constant. 4. Usage occurs continually, but production occurs periodically. 5. the production rate is constant. 6. lead time does not vary. 7. there are no quantity discounts. During the production phase of the cycle- inventory builds up at a rate equal to the difference between production and usage rates. if daily production rate is 20 units and daily usage rate is 5 units so inventory buildup rate is 20-5= 15 units per day. When inventory level builds, when production ceases, the inventory level will begin to decrease. The inventory level will max at the point where production ceases. when amount of inventory on hand is exhausted production is resumed and the cycle repeats. (page 571)

setup costs

the costs involved in preparing equipment for a job when a firm produces its own inventory instead of ordering it from a supplier. these include preparing equipment, adjusting machines, changing cutting tools. These costs are equivalent to ordering costs; they are expressed as a fixed charge per production run regardless of the size of the run (page 562)

Economic order quantity (EOQ)

the order size that minimizes total annual cost. determines How much to order by identifying optimal order quantity by minimizing the sum of certain annual costs that vary with order size and order frequency. Three order size models are 1. the basic economic order quantity model 2. the economic production quantity model. 3. the quantity discount model. (page 566)

fill rate

the percentage of demand filled by the stock on hand (page 584)

When both demand and lead time are variable

the result of squaring the standard deviations of the two previous formulas to obtain their variances, summing them and taking the square root (page 582)

when only lead time is variable

the standard deviation of lead time demand is equal to constant daily demand multiplied by the standard deviation of lead time (page 582)

Benefits of fixed interval system

tight control, grouping yield savings in ordering, packing and shipping costs. practical if inventory withdrawals cannot be closely monitored. (page 588)

Lead time

time interval between ordering and receiving the order might vary, the greater the potential variability, the greater the need for additional stock to reduce the risk of a shortage between deliveries. crucial link between forecasting and inventory management (page 562)

Overall objective of inventory management

to achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds. The decision maker tries to achieve a balance in stocking. he or she must make two fundamental decisions: the timing and size of orders. The greater part of this chapter is devoted to models that can be applied to assist in making those decisions. (page 559)

Requirements for effective inventor management

to be effective management must have the following 1. a system to keep track of the inventory on hand and on oder 2. a reliable forecast of demand that includes an indication of possible forecast error. 3. knowledge of lead times and lead time variability 4. reasonable estimates of inventory holding costs, ordering costs, and shortage costs 5. a classification system for inventory items (page 559)

objective of the quantity discount model

to identify the order quantity that will represent the lowest total cost for the entire set of curves. Two general cases- 1. carrying costs are constant where there will be a single min point at the same quantity and 2. carrying costs are stated as percentage or purchase price and each curve will have a different min point because carrying costs area % of price, lower price will mean lower carrying costs and larger min points. as price decrease each curves min point will be to the right of the next higher curves min point. (page 574) A. When carrying costs are constant all curves have their min points at the same quantity. B. When carrying costs are stated as a percentage of unit price, the min point do not line up. (page 575, figure 13.9 and 13.8)

Holding and ordering costs and annual demand

typically estimated values rather than values that can be precisely determined. Holding costs- sometimes designated by management rather than computed. EOQ- regarded as approx quantity rather than exact. (page 570)